A quote that every worldbuilder worth his salt should know is from Arthur C. Clarke: "Any sufficiently advanced technology is indistinguishable from magic." This is how many of us explain magic, just saying that the civilization is highly advanced and it only appears to be magic.

But what if I wanted to have 'realistic manipulation magic' in the middle ages? Using our (as well as alternate) laws (and theories) of physics, how can I explain the three basic kinds of magic:

Manipulation — Manipulation magic is simply used to create illusions or manipulate the environment, this includes; creating shock-waves or hallucinations, as well as causing fear, nausea or confusion.

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$\begingroup$If you're going to use Destruction and Restoration, why not go all Elder Scrolls and rename Manipulation to Illusion, and add Alteration, Conjuration, and maybe Alchemy?$\endgroup$
– corsiKaFeb 19 '16 at 21:39

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$\begingroup$This is too broad, perhaps you should choose one spell. Tell us what it looks like to an observer and what physical effect it has, then we can find some science for it.$\endgroup$
– SamuelFeb 19 '16 at 21:39

2 Answers
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Manipulation magic: you don't actually see and hear what your eyes and ears see and hear. You see and hear what the brain interprets from your eyes and ears. Perhaps your magic can interfere with signals sent to your brain making you see and hear things that aren't there. Alternatively maybe your magic can bend light to make things invisible or just look different then they actually are.

Destructive magic: matter cannot be created or destroyed but it can be changed from one form to another. Perhaps your magic play on that. Some sort accelerated entropy magic. Or you want to make your mages is really powerful according to Einstein matter could be converted into energy. If you are mages could convert magic to energy with their mind and/or a magic spell then they would be walking nuclear bombs.

Restoration magic: the ability to control someone's body on a cellular level would give your mages the power to cure disease and poisons. They could simply force your cells to produce the correct antibodies or chemicals to counteract whatever disease or poison you had. They might even be able to grow back limbs by forcing your body to produce stem cells and then forcing the stem cells to form a new limb.

More Manipulation magic: maybe your mage or magical creature could release some kind of hallucinogenic hormone into the air. This could cause their enemies to hallucinate their worst fear or greatest desire depending on the hormone used.

More Destructive magic: it's possible for creatures ( such as the electric eel) to have organs that generate electricity. It's also possible for Organic creatures to produce chemicals that when combined together will ignite. This could serve as a biological means for certain "magical" creatures to generate fire or lightning.

This is based on a fundamental assumption that such things can be explained. Simply put, if they could be explained without handwaving, they wouldn't be magic to us.

So you have two choices:

You can handwave and say that the fire coming out of my hands is coming from a reaction with the mana inherent to the area around me and my psi crystals activating... but it really sounds like you don't want to do this.

You can give your people real technology that we, today, understand, but they, in your story, don't. Computer screens, mobile phones, electricity, take any sufficiently advanced technology today and put it in your story. Just don't explain how it works to them.

But you can't have it both ways. You can't have it explained in your story to a scientific, technological sufficiency without also having that explanation work in the real world. And at that point, if it makes so much sense, why don't we have it in the real world?